English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The main contribution of this paper is to prove the subexponential tailequivalence of the stationary queue length distributions in the BMAP/GI/1queues with and without retrials. We first present astochastic-decomposition-like result of the stationary queue length in theBMAP/GI/1 retrial queue, which is an extension of the stochastic decompositionof the stationary queue length in the M${}^X$/GI/1 retrial queue. Thestochastic-decomposition-like result shows that the stationary queue lengthdistribution in the BMAP/GI/1 retrial queue is decomposed into two parts: thestationary conditional queue length distribution given that the server is idle;and a certain matrix sequence associated with the stationary queue lengthdistribution in the corresponding standard BMAP/GI/1 queue (without retrials).Using the stochastic-decomposition-like result and matrix analytic methods, weprove the subexponential tail equivalence of the stationary queue lengthdistributions in the BMAP/GI/1 queues with and without retrials. This tailequivalence result does not necessarily require that the size of an arrivingbatch is light-tailed, unlike Yamamuro's result for the M${}^X$/GI/1 retrialqueue (Queueing Syst. 70:187--205, 2012). As a by-product, the key lemma to theroof of the main theorem presents a subexponential asymptotic formula for thestationary distribution of a level-dependent M/G/1-type Markov chain, which isthe first reported result on the subexponential asymptotics of level-dependentblock-structured Markov chains.

Subexponential tail equivalence of the queue length distributions of BMAP/GI/1 queues with and without retrials